Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913180857401344 |
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| author | Tao, Ran |
| author_facet | Tao, Ran |
| contents | We study the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two. The equation is driven by a Gaussian multiplicative noise. The noise is white in time, smoothed in space at scale $\varepsilon$, and tuned logarithmically by a factor $\frac{1}{\sqrt{\log \varepsilon^{-1}}}$ in its strength. We prove that, after centering and rescaling, the solution random field converges in distribution to an Edwards-Wilkinson limit as $\varepsilon \downarrow 0$. The tool we used here is the Malliavin-Stein's method. We also give a functional version of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_13866 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two Tao, Ran Probability We study the Gaussian fluctuations of a nonlinear stochastic heat equation in spatial dimension two. The equation is driven by a Gaussian multiplicative noise. The noise is white in time, smoothed in space at scale $\varepsilon$, and tuned logarithmically by a factor $\frac{1}{\sqrt{\log \varepsilon^{-1}}}$ in its strength. We prove that, after centering and rescaling, the solution random field converges in distribution to an Edwards-Wilkinson limit as $\varepsilon \downarrow 0$. The tool we used here is the Malliavin-Stein's method. We also give a functional version of this result. |
| title | Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two |
| topic | Probability |
| url | https://arxiv.org/abs/2204.13866 |